Determination of cd and/or md variations from scanning measurements of a sheet of material

ABSTRACT

CD variations and/or MD variations in scan measurements are determined from spectral components of power spectra of scan measurements taken using two or more scanning speeds. Dominant spectral components having the same spatial frequencies identify CD variations and dominant spectral components having the same temporal frequencies identify MD variations. Dominant spectral components are extracted from a noisy power spectrum (PS) by sorting all spectral components into an ordered PS. A first polynomial representing background noise of the ordered PS is used to set a first threshold. Spectral components of the ordered PS that exceed the first threshold are removed to form a noise PS. A second polynomial representing the noise PS is used to set a second threshold. Spectral components of the PS that exceed the second threshold are identified as dominant spectral components of the PS.

FIELD OF THE INVENTION

The invention of the present application discloses a system for thedetermination of cross-machine direction (CD) variations and/or machinedirection (MD) variations within scan measurements taken on a sheet ofmaterial. The disclosed approach compares power spectra of measurementsobtained using two or more scanning speeds with respect to spatialfrequencies for CD variations and with respect to temporal frequenciesfor MD variations. The CD and MD variations are identified by matchingdominant spectral components of power spectra of measurements taken attwo or more scanning speeds with respect to spatial and temporalfrequencies, respectively. The system will be described with referenceto measuring properties of a web of paper as it is being manufacturedfor which it was developed and is initially being used. However, it willbe apparent that it is applicable to the determination of CD and/or MDvariations from measurements of a wide variety of sheet material wherethe sensor(s) and the web are moved perpendicular to one another so thatthe sheet material measurements are obtained by scanning.

BACKGROUND OF THE INVENTION

In a sheet-making process, such as the manufacture of paper, sheetproperties are commonly measured with sensors mounted on a scanner. Thescanner traverses across the forming sheet back and forth while thepaper sheet is moving in the direction perpendicular to the scanner'smotion. A partially broken-away perspective view of a scanning system100 is shown in FIG. 1. A scanner 102 is moved along a supporting framewhich includes two beams 104 positioned one above a web 106 of materialto be scanned and one below the web 106. The scanner 102 includes firstand second members or heads 108, 110 which are moved back-and-forthalong the beams 104 to scan the web 106 in the cross-machine direction(CD) or transversely to the web's direction of movement duringmanufacture. The web 106 of material is moved in the machine direction(MD) or x direction as indicated by the x axis of a coordinate systemshown in FIG. 1 and the cross direction is in the y direction. A gap 112is formed between the first and second heads 108, 110 with the web 106of material to be scanned passing through the gap 112 for the scanningoperation.

The web is sampled by one or more sensors moving along the traversingpath to produce a continuous measurement which is processed to form ascanning measurement of a sheet property across the width of the sheetwhich is referred to as a “scan measurement”. Scan measurements consistof arrays of values that are accumulated over small CD widths called“databoxes” or over short periods of time called “time samples”, eitherof which may sometimes be referred to as “slices”. Ideally, thetraversing paths are perfectly perpendicular to the machine directionand the variation of the entire sheet would be completely captured in amatrix where the MD variation is represented by the average of each scanmeasurement and the CD variation is represented by the shape of the scanmeasurement. In reality, the scan measurements obtained from a scanningsensor capture the sheet property variations along diagonal traversingpaths. The measurement usually cannot be separated in MD and CDvariations easily. The system of the present application enables MD andCD variations in sheet scan measurements to be quickly and effectivelyseparated.

SUMMARY OF THE INVENTION

The system of the present application determines cross-machine direction(CD) variations and/or machine direction (MD) variations within scanmeasurements of a sheet of material being measured, for example a sheetof paper, based on spectral components of power spectra of scanmeasurements taken using two or more scanning speeds. Dominant spectralcomponents having the same spatial frequencies are used to identify CDvariations and dominant spectral components having the same temporalfrequencies are used to identify MD variations.

In accordance with one aspect of the invention of the presentapplication, a process for determining CD variations from scanningmeasurements made of a sheet of material comprises scanning at least onesensor over a sheet of material at a first scanning speed to generatefirst scan measurements. The first scan measurements are transformedinto a first spatial power spectrum with respect to a first spatialfrequency and first spatial dominant spectral components of the firstspatial power spectrum are detected. At least one sensor is scanned overthe sheet of material to be measured at a second scanning speed togenerate second scan measurements. The second scan measurements aretransformed into a second spatial power spectrum with respect to asecond spatial frequency and second spatial dominant spectral componentsof the second spatial power spectrum are detected. CD spectralcomponents of the scanning measurements are identified by determining atleast one of the first spatial dominant spectral components that are atthe same spatial frequency as at least one of the second spatialdominant spectral components.

The first spatial frequency of the process may be equal to the secondspatial frequency.

The process may further comprise scanning at least one sensor over asheet of material to be measured at a third scanning speed to generatethird scan measurements. The third scan measurements are transformedinto a third spatial power spectrum with respect to a third spatialfrequency. Third spatial dominant spectral components of the thirdspatial power spectrum are detected. The CD spectral components of thescanning measurements are identified by determining at least one of thefirst spatial dominant spectral components that are at the same spatialfrequency as at least one of the second spatial dominant spectralcomponents and at least one of the third spatial dominant spectralcomponents.

The CD variations within the scanning measurements can be constructedusing inverse transformation of the CD spectral components. The step ofdetecting first spatial dominant spectral components of the firstspatial power spectrum may comprise sorting all spectral components fromthe first spatial power spectrum in order of magnitude to form a firstordered spatial power spectrum. Background noise of the first orderedspatial power spectrum can be represent with a first polynomial. A firstdeviation threshold may be set with respect to the first polynomial andspectral components of the first ordered spatial power spectrum may becompared to the first deviation threshold. Spectral components of thefirst ordered spatial power spectrum that exceed said first deviationthreshold are removed from the first ordered spatial power spectrum toform a first noise spatial power spectrum. The first noise spatial powerspectrum in the first spatial power spectrum is represented by a secondpolynomial. A second deviation threshold is set with respect to thesecond polynomial and spectral components of the first spatial powerspectrum that exceed the second deviation threshold are identified asfirst spatial dominant spectral components of the first spatial powerspectrum. Commonly the first and second polynomials are low-orderpolynomials.

The step of detecting second spatial dominant spectral components of thesecond spatial power spectrum may comprise sorting all spectralcomponents from the second spatial power spectrum in order of theirmagnitudes to form a second ordered spatial power spectrum. Backgroundnoise of the second ordered spatial power spectrum is represented by athird polynomial. A third deviation threshold is set with respect to thethird polynomial and spectral components of the second ordered spatialpower spectrum are compared to the third deviation threshold. Spectralcomponents of the second ordered spatial power spectrum that exceed thethird deviation threshold are removed from the second spatial powerspectrum to form a second noise spatial power spectrum. The second noisespatial power spectrum is represented by a fourth polynomial and afourth deviation threshold is set with respect to the fourth polynomial.Spectral components of the second spatial power spectrum that exceed thefourth deviation threshold are identified as second spatial dominantspectral components of the second spatial power spectrum.

The process may further comprise transforming the first scanmeasurements into a first temporal power spectrum with respect to afirst temporal frequency. First temporal dominant spectral components ofthe first temporal power spectrum are detected and the second scanmeasurements are transformed into a second temporal power spectrum withrespect to a second temporal frequency. Second temporal dominantspectral components of the second temporal power spectrum are detectedand MD spectral components of the scanning measurements are identifiedby determining at least one of the first temporal dominant spectralcomponents that is at the same temporal frequency as at least one of thesecond temporal dominant spectral components. The process may furthercomprise constructing the CD variations within the scanning measurementsby inverse transformation of the CD spectral components, andconstructing the MD variations within the scanning measurements byinverse transformation of the MD spectral components.

In accordance with another aspect of the invention of the presentapplication, a process for determining MD variations from scanningmeasurements made of a sheet of material may comprise scanning at leastone sensor over a sheet of material to be measured at a first scanningspeed to generate first scan measurements. The first scan measurementsare transformed into a first temporal power spectrum with respect to afirst temporal frequency and first temporal dominant spectral componentsof the first temporal power spectrum are detected. At least one sensoris scanned over the sheet of material to be measured at a secondscanning speed to generate second scan measurements. The second scanmeasurements are transformed into second temporal power spectrum withrespect to a second temporal scanning frequency. Second dominantspectral components of the second temporal power spectrum are detected.The MD spectral components of the scanning measurements are identifiedby determining at least one of the first temporal dominant spectralcomponents that is at the same temporal frequency as at least one of thesecond temporal dominant spectral components.

The process may further comprise constructing the MD variations withinthe scanning measurements by inverse transformation of the MD spectralcomponents. The process may further comprise transforming the first scanmeasurements into a first spatial power spectrum with respect to a firstspatial frequency; detecting first spatial dominant spectral componentsof the first spatial power spectrum; transforming the second scanmeasurements into a second spatial power spectrum with respect to asecond spatial frequency; detecting second spatial dominant spectralcomponents of the second spatial power spectrum; and identifying CDspectral components of the scanning measurements by determining at leastone of the first spatial dominant spectral components that is at thesame spatial frequency as at least one of the second spatial dominantspectral components.

The process may further comprise constructing the MD variations withinsaid scanning measurements by inverse transforming the MD spectralcomponents; and constructing the CD variations within the scanningmeasurements by inverse transformation of the CD spectral components.

In accordance with an additional aspect of the invention of the presentapplication, a process for extracting dominant spectral components froma power spectrum of noisy measurements may comprise sorting all spectralcomponents from a power spectrum in order of magnitude to form a firstordered power spectrum; representing background noise of the orderedpower spectrum with a first polynomial; setting a first threshold withrespect to the first polynomial; comparing spectral components of theordered power spectrum to the first threshold; removing spectralcomponents of the power spectrum that exceed the first threshold fromthe ordered power spectrum to form a noise power spectrum; representingthe noise power spectrum in the power spectrum with a second polynomial;setting a second threshold with respect to the second polynomial; and,identifying spectral components of the power spectrum that exceed thesecond threshold as dominant spectral components of the power spectrum.The first and second polynomials may be low-order polynomials.

BRIEF DESCRIPTION OF THE DRAWINGS

The benefits and advantages of the invention of the present applicationwill become apparent to those skilled in the art to which the inventionrelates from the subsequent description of the illustrated embodimentsand the appended claims, taken in conjunction with the accompanyingdrawings, in which:

FIG. 1 is partially broken-away perspective view of a scanning system;

FIG. 2(a)-FIG. 2(c) show illustrative scanning speed patterns for use oftwo different scanning speeds of a scanning system;

FIG. 3 shows the use of two scanning systems operating at two differentscanning speeds;

FIG. 4 shows a simulated sheet of material with CD variations only andthe traces of four scans made at two different scan speeds on thesimulated sheet;

FIG. 5 shows scan measurements of the simulated sheet of FIG. 4 obtainedusing the scans shown in FIG. 4 having two different scan speeds;

FIG. 6 is the spatial spectra of the scan measurements of FIG. 5;

FIG. 7 shows a simulated sheet of material with MD variations only andthe traces of four scans made at two different scan speeds on thesimulated sheet;

FIG. 8 shows scan measurements of the simulated sheet of FIG. 7 obtainedusing the scans shown in FIG. 7 having two different scan speeds;

FIG. 9 is the spatial spectra of the scan measurements of FIG. 8;

FIG. 10 is the spatial spectra of FIG. 9 converted to temporalfrequencies using the measurement scan speeds;

FIG. 11 is a simulated sheet of material with both MD and CD variationsand the traces of scans made using two different scan speeds;

FIG. 12 shows scan measurements of the simulated sheet of FIG. 7obtained using the scans shown in FIG. 7 having two different scanspeeds;

FIG. 13 is the spatial spectra of the scan measurements of FIG. 12;

FIG. 14 is the spatial spectra of FIG. 13 converted to temporalfrequencies using the measurement scan speeds;

FIG. 15 illustrates a scan measurement, the CD and MD variations in thescan measurement determined using the process of the present applicationand the background random noise in the scan measurement found byremoving the CD and MD variations from the scan measurement;

FIG. 16(a) illustrates a measurement that contains only random noise;

FIG. 16(b) illustrates the derived power spectrum of the measurement ofFIG. 16(a);

FIG. 17(a) illustrates a measurement that contains specific signals (orvariations) at several frequencies and background random noise;

FIG. 17(b) illustrates the derived power spectrum of the measurement ofFIG. 17(a);

FIG. 18 illustrates a measurement which may contain a few dominantspectra;

FIG. 19 illustrates the power spectrum of the measurement of FIG. 18;

FIG. 20 shows the spectral components of power spectrum of FIG. 19 thathave been sorted and placed in descending order based on theirmagnitudes; and

FIG. 21 illustrates a noise spectrum determined from the ordered powerspectrum of FIG. 20 and dominant spectral components of the powerspectrum of the measurement of FIG. 18 determined in accordance with oneaspect of the present application.

DETAILED DESCRIPTION OF THE INVENTION

The system of the present application will be described with referenceto measuring properties of a web of paper as it is being manufacturedfor which it was developed and is initially being used. In this regard,the system can be used to measure properties not only of sheet-makingprocesses but also rewinding processes, coating machines, and many othersimilar processes and machines where scan measurements are commonlymade. In addition, the system of the present application can be used foranalysis of measurements that are obtained by generally perpendicularrelative movement between a sheet of material to be measured and one ormore sensors however that movement is affected. The disclosed systemeffectively separates the MD and/or CD variations in scan measurements.Since the separated MD and/or CD variations are more accurate than thosedetermined by known prior art systems, the separated variations can beused as inputs to corresponding MD and/or CD controllers to bettercontrol processes being measured. The frequencies of the separated MDand/or CD variations can also be used to determine the root causes ofthe variations. Reconstructed MD and/or CD variation patterns, whichmight not be recognized directly from the scanning measurements, areuseful tools in determining potential improvements if the identifiedvariations are eliminated or substantially reduced.

Since scanning sensors have been used online to measure sheet propertiesfor many years, it is understood that the scan measurements obtainedfrom the zigzag path of the sensors mixes MD, CD and localizedvariations together. The separation of MD and CD variations from a scanmeasurement has always been a challenge. Traditionally, the MD variationcomponent has been approximated by averaging the scan measurements andthe CD variation component has been estimated by filtering subsequentscans at each databox. The approximated MD variation component would notcontain any MD variations that are faster than the scan time and theapproximated CD variation component is likely to be contaminated ordistorted by those faster MD variations.

Several approaches have been used to overcome the challenge ofseparating MD variations and CD variations from scan measurements. As afirst approach, scanning has been eliminated all together by usingfull-width, non-scanning measurement systems, see for example U.S. Pat.No. 5,563,809. In principle, this is an ideal solution. However, thecost and complexity of non-scanning measuring systems often out-weightsthe benefits that are expected to be gained from such systems. A fewnon-scanning systems have been designed in the past, but for the mostpart, they were not commercially accepted.

A second approach has been to scan faster, scan local regions, or mixscanning with single point measurements. These approaches shift thevariation contents to be detected depending on the scan speed, theregions or the single points that are scanned. However, the fundamentalchallenge remains the same.

A third approach has been to process MD and CD separation morefrequently, for example every 5 seconds instead of every 20-30 secondsin accordance with typical scan times. This approach of using morefrequent processing of scan measurement data provides estimates of MDvariations that are faster than the scan time thus improving theseparation of MD and CD variation components. Unfortunately, suchtime-based estimation improvements still cannot detect MD variationsthat are shorter than the sampling time, such as 5 seconds.

The system for determination of CD and/or MD variations from scanningmeasurements of a sheet of material of the present application addressesthe challenge of separating MD variations and CD variations from scanmeasurements and avoids the shortcomings of existing approaches. Thescan measurement obtained from a scanning sensor can be transformed intothe spectral domain by the well-known Fourier transformation techniqueimplemented using a Fast Fourier Transform (FFT) algorithm or a DiscreteFourier Transform (DFT) algorithm. A wide variety of programs arecommercially available for performing FFT and DFT, accordingly they willnot be described further herein.

When scan measurements are taken over small CD widths, i.e.,“databoxes”, and hence expressed in databox resolution, the spatial (CD)frequency is derived from the databox resolution directly and thetemporal (MD) frequency is obtained from the spectral frequency and thescan speed. For example, assuming a constant scan speed, the spatialfrequency of a scan measurement that records its values in 600 databoxesacross the width of the sheet, the spatial frequency ranges between0.001667 and 0.50 (1/databox). On the other hand, the temporal (MD)frequencies of the same measurement are derived by multiplying thespatial frequencies with the scan speed. For example, the temporalfrequency of a scan measurement obtained with a 30 databoxes/sec scanspeed and a resolution of 600 databoxes ranges between 30·0.001667=0.05Hz and 30·0.5=15 Hz.

Alternatively, when scan measurements are taken over short periods oftime, i.e., “time samples”, the temporal (MD) frequency is deriveddirectly and the spatial (CD) frequency is obtained from the temporalfrequency and the scan speed. For example, the temporal frequency of ascan measurement that is expressed in 1 millisecond time samples with a20 second scan time at a constant scan speed, ranges between 0.05 Hz and500 Hz. The spatial (CD) frequencies of the same measurement areobtained by dividing the temporal frequencies with the scan speed, forexample 30 databoxes/sec. The spatial frequency of the same scanmeasurement ranges between 0.05/30=0.001667 and 500/30=16.67(1/databox).

For a sheet of material that consists of persistent CD variations (pureCD variations), dominant spectral components in the CD direction withrespect to their spatial frequencies will not change for differentscanning speeds so that scan measurements taken at two or more differentscanning speeds should yield the same dominant spatial spectralcomponents. By comparing the spatial spectral content of scanmeasurements taken at two or more scan speeds, dominant spatial spectralcomponents from the different scan measurements will be found at thesame spatial frequencies. This overlap of the dominant spatial spectralcomponents represents the CD spectral contents. Accordingly, using thesystem of the present application, the CD spectral contents in scanmeasurements can be identified and separated from the scan measurements.

On the other hand, for a sheet of material that consists of persistentMD variations (pure MD variations), dominant spectral components of MDvariations obtained by scanning the sheet at two or more scanning speedsare not aligned with respect to the same spatial frequencies. However,when the spectral contents of scan measurements are shown with respectto their temporal frequencies, the dominant temporal spectral componentswill appear at the same temporal frequencies regardless of the scanspeed. By comparing the spectral contents of scan measurements made attwo or more scanning speeds with respect to temporal frequencies, theoverlap of the dominant temporal spectral contents can be detected.Accordingly, using the system of the present application, the MDspectral contents in scan measurements can be identified and separatedfrom the scan measurements.

After both MD and CD dominant spectral contents and their spatial andtemporal frequencies are identified, inverse transformation, including,for example, the inverse Fourier transformation, can be used to separateMD and CD variation components from each scan measurement. The MD and CDdominant spectral components and their spatial and temporal frequenciescan be identified regularly, intermittently, or on an event-driven basiswhile the separation of MD and CD variations from each scan measurementcan be performed as frequently as needed to achieve optimal performanceof the process that is being measured. The MD and CD dominant spectralcomponents and their spatial and temporal frequencies can be identifiedfor the full width of sheet or any portion of sheet while the separationof MD and CD variations from each scan measurement can also be performedaccordingly to meet the needs of the associated control and/ordiagnostic applications.

An example of a series of operations that can be performed for operationof the system of the present application will now be described followedby simulated examples illustrating the basic principles used in thepresent application to ensure complete understanding of operation of thesystem of the present application.

1. Scan at least one sensor over a moving sheet with at least twoscanning speeds which can be interleaved periodically, arranged bygroups or can be event driven. FIG. 2 (a) illustrates groups ofdifferent scanning speeds showing two scans at a scanning speed of V₁interleaved with two scans at a scanning speed of V₂. FIG. 2(b)illustrates alternating scans of different scanning speeds showingalternating scans at V₁ and V₂ scanning speeds. FIG. 2(c) illustratesrandom alternation of scanning speeds. Other arrangements for scanningwith at least two scanning speeds will be apparent to those skilled inthe art. For example two separate scanners, one scanning at a scan speedof V₁ and one scanning at a scan speed of V₂ are shown in FIG. 3. Thus,while the system of the present application is described with referenceto a single scanner that is scanned at two scanning speeds, a singlescanner that scans at more than two scanning speeds can be used. Alsotwo or more scanners can be used with each scanner having similarsensors and scanning at one, two or more than two scanning speeds.

2. Scan measurements from the scanning sensor(s) and their correspondingscan speeds can be recorded as needed for processing scan measurements.

3. The scan measurements are transformed to their corresponding powerspectra using, for example, Fourier transformation.

4. Dominant spectral components are detected from the transformed powerspectra and their frequencies noted. Spatial (CD) frequency is based onthe databox resolutions of the scanning operations and temporal (MD)frequency is based on the temporal sampling frequencies and the scanspeeds of the scanning operations. A novel process for the extraction ofdominant spectral components from noisy measurements will be describedbelow.

5. The power spectra of the scan measurements at the different scanspeeds are compared against their spatial frequencies or overlaid toidentify the dominant spectral components that appear at the samespatial frequencies in both scan measurements to identify the CDspectral components.

6. The CD variations can be constructed using inverse transformation,for example, inverse Fourier transformation, of the identified CDspectral components.

7. The power spectra of the scan measurements at the different scanspeeds are compared against their corresponding temporal frequencies oroverlaid to identify the dominant spectral components that appear at thesame temporal frequencies in both scans to identify the MD spectralcomponents

8. The MD variations can be constructed using inverse transformation,for example, inverse Fourier transformation, of the identified MDspectral components.

9. The residual variations can be derived as the remainder after boththe MD and CD variations are separated from each measurement.

The first simulated example is one where the sheet has only CDvariations and two different scan speeds are used (20 second scans and25 second scans—for 600 databox spatial resolution, these scan speedscorrespond to 30 databoxes/sec and 24 databoxes/sec, respectively). Asheet with CD variations only and the traces of scans made using twoscan speeds are shown in FIG. 4. The trace of each scan speed is markedwith a diagonal line—the bottom or first two scans 200, 202 (solidlines) are 20 second scans, and the two top or last scans 204, 206(dotted lines) are 25 second scans.

Scan measurements 200S, 202S (shown as solid lines) and 204S, 206S(shown as dotted lines) obtained from FIG. 4 with two different scanspeeds and their spatial spectra are plotted in FIG. 5 and FIG. 6,respectively. The dominant CD spectral components 207SS, 209SS, shown assolid and dotted lines, respectively, from the spectra appear at thesame spatial frequency of 0.015 (1/databox).

The second simulated example is one where the sheet has only MDvariations and again two different scan speeds are used (20 second scansand 25 second scans—for 600 databox spatial resolution, these scanspeeds correspond to 30 databoxes/sec and 24 databoxes/sec,respectively). A sheet with MD variations only and the traces of scansmade using two scan speeds are shown in FIG. 7. The trace of each scanspeed is marked with a diagonal line—the bottom or first two scans 210,212 (solid lines) are 20 second scans and the top or last two scans 214,216 (dotted lines) are 25 second scans.

Scan measurements 210S, 212S (shown as solid lines) and 214S, 216S(shown as dotted lines) obtained from FIG. 7 with two different scanspeeds and their spatial spectra are plotted in FIG. 8 and FIG. 9,respectively. The dominant MD spatial spectral components 217SS, 219SSfrom the spectra, shown as dotted and solid lines, respectively, appearat different spatial frequencies of 0.0053 and 0.0067 (1/databox).

However, by converting the dominant MD spectral components 217SS, 219SSfrom the spatial spectra to temporal frequencies using theircorresponding scan speeds as described earlier, the dominant MD spectralcomponents 217TS, 219TS appear at the same temporal frequency of 0.16 Hzas shown in FIG. 10 as dotted and solid lines, respectively.

The third simulated example is one where the sheet has both MD and CDvariations and again two different scan speeds are used (20 second scansand 25 second scans—for 600 databox spatial resolution, these scanspeeds correspond to 30 databoxes/sec and 24 databoxes/sec,respectively). A sheet with both MD and CD variations and the traces ofscans made using two scan speeds are shown in FIG. 11.

The trace of each scan speed is marked with a diagonal line—the bottomor first two scans 230, 232 (solid lines) are 20 second scans and thetwo top or last two scans 234, 236 (dotted lines) are 25 second scans.Scan measurements 230S, 232S (solid lines) and 234S, 236S (dotted lines)obtained from FIG. 11 with two different scan speeds and their spatialspectra are plotted in FIG. 12 and FIG. 13, respectively. The dominantCD spectral components 237SS, 239SS, shown as dotted and solid lines,respectively, from the spectra appear at the same spatial frequency of0.015 (1/databox). The dominant MD spatial spectral components 237′SS,239′SS from the spectra, shown as dotted and solid lines, respectively,appear at different spatial frequencies of 0.0053 and 0.0067(1/databox).

When the dominant CD and MD spectral components 237SS, 239SS, 237′SS,239′SS are converted to temporal frequencies using their correspondingscan speeds as described earlier, the MD dominant spectral components237′SS (dotted line), 239′SS (solid line) appear at the same temporalfrequency of 0.16 Hz, and the CD spectral components 237SS (dotted line)and 239SS (solid line) appear at different temporal frequencies of 0.36Hz and 0.45 Hz as shown in FIG. 14.

Thus, when the spectra of scan measurements obtained from different scanspeeds are shown with respect to the spatial frequencies (FIG. 13), thedominant spectral components that appear at the same spatial frequencyrepresent the CD variation components. Similarly, when the spectra ofscan measurements obtained from different scan speeds are shown withrespect to their corresponding temporal frequencies (FIG. 14), thedominant spectral components that appear at the same temporal frequencyrepresent the MD variation components. This result allows effectiveidentification and separation of the CD and MD variations from sheetscan measurements that consist of both CD and MD variations.

For example, once the scan measurements of FIG. 12 have been processedas described above to identify the CD and MD variation components in thespectral domain, those variation components can be inverse transformedinto the CD variations 242 and the MD variations 244 shown in FIG. 15.The CD variations 242 and the MD variations 244 can then be removed fromthe scan measurement, for example the scan measurement 230S shown inFIG. 15, to obtain the background random noise 246 in the scanmeasurement 230S. The CD variations 242 can be used as inputs to a CDcontroller and the MD variations 244 can be used as inputs to an MDcontroller to better control processes being measured. The frequenciesof the separated CD and MD variations 242, 244 can also be used todetermine the root causes of those variations so that the causes can beaddressed and thereby those variations eliminated or substantiallyreduced.

As noted earlier, a process for extracting dominant spectra from a noisymeasurement will now be described. In many real world applications, ameasurement typically contains both a useful signal and backgroundrandom noise. For practical purposes, there is always a strong need toseparate the useful signal from its background random noise. Thechallenge is that it is not obvious how to distinguish between theuseful signal and the background noise directly from the measurementitself. In practice, very often a measurement can be transformed intothe spectral domain using, for example, Fourier transformation tofacilitate differentiation between the signal and the background noise.In the spectral domain, the useful signal of the original measurementoften shows up as a set of dominant spectra in the power spectrum. Anovel process for effectively extracting the dominant spectra from thepower spectrum of a given measurement which can be used in the systemfor determination of CD and/or MD variations from scanning measurementsof a sheet of material of the present application will now be described.

The dominant spectra extraction process can be used when working with avariety of measurements including without limitation measurements takenby industrial instrumentation, research laboratory apparatus, medicalequipment, communication equipment, and measurements of commercialnumerical trends, any historical data series and all forms ofmulti-dimensional arrays of data. Wherever the measurements are takenand to whatever the measurements apply, the disclosed processeffectively identifies/separates the dominant spectral components in themeasurements from their background random noise. The extracted dominantspectral components are noise-free and can be used to determine the rootcauses of the dominant spectra or to reconstruct the dominant variationsthat are hidden in the measurements as described above with regard toFIG. 15.

Power spectrum analysis is a well-known tool to analyze the spectralcontents of measurements. If a measurement contains only random noise,then its power spectrum should have uniform magnitudes at allfrequencies. If the spectrum is non-uniform, then there must be a fewspectral components larger than the rest. These larger spectralcomponents are the “dominant spectra” in the given measurement and theyoften represent the useful signal in the given measurement. To separatethe dominant spectra, you need to know the magnitude of the noiseaccurately. However, the magnitude of the noise cannot be accuratelyestimated if the dominant spectra are not separated from themeasurement. Thus, a catch-22 situation is the result.

Although it may be relatively easy to “visually” pick out the dominantspectra from a power spectrum of a measurement, it is notstraightforward for an instrument or a computer to systematically pickout the dominant spectra. The dominant spectra can occur at anyfrequency and have various magnitudes. It is non-trivial to separatedominant spectra from a signal's background random noise. This aspect ofthe present application overcomes these problems and enables machineextraction of the dominant spectra from a spectrum of a measurementusing estimation and threshold setting techniques.

Given a measurement as a sequence of sampled data, the power spectrum ofthe measurement can be obtained using a Fast Fourier Transformation(FFT) or Discrete Fourier Transformation (DFT) algorithm. If themeasurement 300 contains only random noise as shown in FIG. 16(a), thenits derived power spectrum 302 is substantially uniform across itsentire frequency range as shown in FIG. 16(b).

If the measurement 304 contains specific signals (or variations) atseveral frequencies as shown in FIG. 17(a), its power spectrum 306 asseen in FIG. 17(b) will show spikes 308 at those frequencies. Thespectral components which are larger than the rest and marked withcircles 310 in FIG. 17(b) are the “dominant spectra” of the signals inthe measurement. These “dominate spectra” can be systematicallyextracted using the process for extracting dominant spectra from a noisymeasurement in accordance with this present aspect of the presentapplication.

An example of a series of operations that can be performed forextraction of dominant spectra or spectral components from measurementswill now be described followed by an example illustrating the basicprinciples used in the present application to ensure completeunderstanding of operation of the dominant spectra extraction process ofthe present application.

1. Sort all spectral components from the original power spectrum inorder of their magnitudes and keep their sorting order.

2. Approximate the background noise of the sorted spectrum with a firstpolynomial, typically a low order polynomial.

3. Identify the outlier spectral components that significantly deviatefrom the first low-order polynomial.

4. Remove the outlier spectral components identified in operation 3 fromthe original power spectrum. The remaining spectral components representthe background noise of the original power spectrum.

5. Approximate the remaining spectral components from operation 4representative of the background noise of the original power spectrumwith a second polynomial, typically a low order polynomial.

6. Extract the spectral components that significantly deviate from thesecond polynomial, typically a low-order polynomial. The extractedspectral components are the dominant spectral components of the originalpower spectrum.

An example for extraction of dominant spectra or spectral componentsfrom actual measurements makes reference to FIG. 18 which illustrates ameasurement 312 which may contain a few dominant spectra.

FIG. 19 illustrates the power spectrum 314 of the measurement 312 shownin FIG. 18. Even though a few dominant spectra are visually noticeablein FIG. 19, it is nontrivial to consistently identify all dominantspectra that meet desired criteria from a power spectrum ofmeasurements. One simple approach that might be used is to set a uniformthreshold across the entire spectrum. Unfortunately, such a uniformthreshold would not work well because background random noise could haveslightly higher spectra near the low frequency range.

FIG. 20 shows the spectral components of FIG. 19 that have been sortedand placed in descending order based on their magnitudes. The generallyflat region 316 of the resulting ordered spectrum 318, approximatelyfrom spectral frequency 0.05 to spectral frequency 0.5 of FIG. 20, isthe region of the spectrum that represents background noise of themeasurement and that generally flat region is approximated using alow-order first polynomial. A first threshold is set relative to thefirst polynomial as shown by the dashed line 320. The first thresholdcan be set by selecting a distance from the first polynomial, forexample set in relation to the standard deviation σ₁ of the statisticaldistribution of the spectral components that comprise the generally flatregion of the ordered spectrum of FIG. 20 with respect to theircorresponding first polynomial reference. Currently, it is believed thatthe first threshold could be within a range of about σ₁ to 10σ₁. Theoutlier spectra that significantly deviate from the first polynomial andexceed the first threshold (shown as circles in FIG. 20) include thedominant spectral components of the power spectrum and are removed fromthe ordered spectrum to form a noise spectrum.

The noise spectrum 322, shown as dots in FIG. 21, is used to approximatethe background noise in the original power spectrum 314. As is typical,a low-order second polynomial 324 approximation is made of the noisespectrum shown in FIG. 21. A second threshold 326 is set relative to thesecond polynomial 324 as shown by the dashed line 326 in FIG. 21. Thesecond threshold 326 can be set by selecting a distance from the secondpolynomial 324, for example the second threshold 326 can be setaccording to the statistical distribution of the background noiseapproximated by the noise spectrum 322. The dashed line 326 in FIG. 21is set at three times the standard deviation, 3σ₂, of the backgroundnoise with respect to the second polynomial 324. The second threshold326 can be adjusted to provide the best results for the dominant spectraextraction process of the present application. Currently, it is believedthat the second threshold could be within a range of about 3σ₂ to 6σ₂.

In FIG. 21, the spectra (represented by circles within the dotted line328) which are above the dashed threshold 326 so that they deviatesignificantly from the background noise or noise spectrum 322 areidentified as the dominant spectra within the power spectrum.

The selection of the first and second polynomials and the first andsecond thresholds provide tuning parameters for the dominant spectraextraction process of the present application.

The dominant spectra extraction process of the present application canbe used in many different applications. For example, if the originalmeasurement is a flow rate of a pipe in a chemical plant, the frequencyof an extracted dominant spectral component might be matched to anoscillation frequency of a control valve so that an alarm can be givento check the control valve so see whether it may be malfunctioning andin need of repair or replacement.

If the original measurement consists of multiple dominant spectralcomponents, for example as shown in FIG. 21, the dominant spectraextraction process of the present application can be used to extractthem all so that they can be used to trace each individual dominantspectral component to its root-cause. The root causes can be a number ofdifferent valves, pumps, other rotating devices and the like.

When dominant spectra are extracted using the disclosed dominant spectraextraction process of the present application, they can be used toreconstruct their original signals by applying inverse transformations,such as inverse Fourier transformation, to the dominant spectra. Theresulting reconstructed signals can be used for control or forestimating potential improvement if the dominant spectra are eliminated.

The disclosed processes are easy to use and very effective at pickingout the dominant spectra systematically for a wide variety ofmeasurements.

Although the invention of the present application has been describedwith particular reference to certain illustrated embodiments thereof,variations and modifications of the present invention can be effectedwithin the spirit and scope of the following claims.

For example, the disclosed process for determining CD and/or MDvariations from scan measurements of a sheet of material can be appliedto a single scanner frame that scans at two or more scanning speeds, twoor multiple scanner frames that scan at different scanning speeds whereeach scanner frame hosts a similar sensor, or two or multiple framesthat scan at two or multiple scanning speeds on each frame. Temporalresolution (number of samples per second) and/or spatial resolution(number of databoxes) from each sensor on each frame does not have to bethe same. In reality, the spatial resolution is set to be the same tokeep the system simpler. The disclosed process does not always have tobe applied to entire scan measurements. Rather, this process can beapplied to any portion of the scan measurements. If the disclosedprocess is applied to a sensor that scans at two or multiple scanningspeeds, the order of the scanning speeds can be arranged in manydifferent ways in addition to those illustrated in FIGS. 2(a), 2(b) and2(c) which show three different examples: V1, V1, V2, V2, V1, V1 . . .(block); V1, V2, V1, V2, V1 . . . (alternating); and V1, V2, V1, V1, V2,V1, V2, V2 . . . (random). The power spectra of scan measurements can beupdated or accumulated with the scan measurements of the same scanningspeed either regularly, intermittently or in a batch. The process ofdetermining

MD and CD spectral components and frequencies does not have to be fullysynchronized with the update of the scan measurements or the separationof MD and CD variations from scan measurements. However, thedetermination of MD and CD frequencies is needed before the inversetransformation can be applied to separate MD and CD variations. Thedetermination of MD and/or CD spectral components can be triggered byevents or executed periodically by measurement updates but the actualseparation of CD and MD variations from the scan measurements mostlikely will be executed regularly whenever scan measurements areupdated.

What is claimed is: 1.-12. (canceled)
 13. A process for extractingdominant spectral components from a power spectrum of noisy measurementscomprising: sorting all spectral components from a power spectrum inorder of magnitude to form an ordered power spectrum; representingbackground noise of said ordered power spectrum with a first polynomial;setting a first threshold with respect to said first polynomial;comparing spectral components of said ordered power spectrum to saidfirst threshold; removing spectral components of said power spectrumthat exceed said first threshold from said ordered power spectrum toform a noise power spectrum; representing said noise power spectrum insaid power spectrum with a second polynomial; setting a second thresholdwith respect to said second polynomial; and identifying spectralcomponents of said power spectrum that exceed said second threshold asdominant spectral components of said power spectrum.
 14. The process asclaimed in claim 13 wherein said first and second polynomials arelow-order polynomials.